In this study, we
investigate the feasibility of a multi-pixel scheme in the inversion of
aerosol optical properties for multispectral satellite instruments over the
ocean. Different from the traditional satellite aerosol retrievals conducted
pixel by pixel, we derive the aerosol optical
thickness (AOT) of multiple pixels simultaneously by adding a smoothness
constraint on the spatial variation of aerosols and oceanic substances, which
helps the satellite retrieval, with higher consistency from pixel to pixel.
Simulations are performed for two representative oceanic circumstances, open
and coastal waters, as well as the land–ocean interface region. We retrieve
the AOT for fine, sea spray, and dust aerosols simultaneously using synthetic
spectral measurements, which are from the Greenhouse Gases Observing
Satellite and Thermal and Near Infrared Sensor for Carbon Observation –
Cloud and Aerosol Imager (GOSAT∕TANSO-CAI), with four wavelengths ranging
from the ultraviolet to shortwave infrared bands. The forward radiation
calculation is performed by a coupled atmosphere–ocean radiative transfer
model combined with a three-component bio-optical oceanic module, where the
chlorophyll a concentration, sediment, and colored dissolved organic matter
are considered. Results show that accuracies of the derived AOT and spectral
remote-sensing reflectance are both improved by applying smoothness
constraints on the spatial variation of aerosol and oceanic substances in
homogeneous or inhomogeneous surface conditions. The multi-pixel scheme can
be effective in compensating for the retrieval biases induced by measurement
errors and improving the retrieval sensitivity, particularly for the fine
aerosols over the coastal water. We then apply the algorithm to derive AOTs
using real satellite measurements. Results indicate that the multi-pixel
method helps to polish the irregular retrieved results of the satellite
imagery and is potentially promising for the aerosol retrieval over highly
turbid waters by benefiting from the coincident retrieval of neighboring
pixels. A comparison of retrieved AOTs from satellite measurements with those
from the Aerosol Robotic Network (AERONET) also indicates that retrievals
conducted by the multi-pixel scheme are more consistent with the AERONET
observations.

Aerosols are one of the largest uncertainty factors in estimations and
interpretations of the Earth's changing energy budget (Boucher et al.,
2013). They exert significant and complex impacts on the radiation process
through both direct and indirect effects and have detrimental
influences on the air quality and public health. Since the ocean covers more than 70 % of the Earth's surface, it is indispensable to estimate the
aerosol loading over the ocean. Due to the limitation of spatial and
temporal coverage from ground-based measurements, satellite remote sensing
has been the most efficient approach for observing the variation of aerosols
over wide areas and with fine spatiotemporal resolution.

In the atmosphere–ocean system, the total radiance measured by a
satellite-borne sensor at the top of atmosphere mostly comes from the
atmospheric scattering, and the oceanic contribution generally accounts
for ∼ 10 % of the satellite signal over open and non-glint ocean regions. In the 1990s, there were useful retrievals of aerosol
optical thickness (AOT) over the global ocean, derived from the Advanced Very
High Resolution Radiometer (AVHRR) generated by NOAA (Stowe et al., 1992).
Moreover, Nakajima and Higurashi (1997) and Mishchenko et al. (1999)
propose improved two-channel methods for deriving more information on aerosols
using red and near-infrared band (NIR) measurements from the AVHRR. With the
advances in the satellite instrument, several improved algorithms have also
been developed using more channels that cover band ranges from ultraviolet (UV) to NIR or shortwave infrared (SWIR) to retrieve both AOT and aerosol
type (Tanré et al., 1997; Torres et al., 1998; Higurashi and Nakajima,
2002; Remer et al., 2005; Kim et al., 2007; Lee et al., 2012; Wang et al.,
2017; Choi et al., 2018) or layer height (Xu et al., 2017). These algorithms
have been successfully adopted in the operational processing of aerosol
retrieval for polar or geostationary satellite instruments with good
accuracies. In addition, multiple angular or polarization measurements are
conducive for deriving aerosol properties by providing more information
content over the ocean (Martonchik et al., 1998; Goloub et al., 1999). As
for the ocean color (OC) retrieval, such as that used in the Sea-Viewing
Wide Field-of-View Sensor, an atmospheric correction scheme is always adopted
to derive the AOT from sets of candidate aerosol modes based on the satellite
measurements at red or NIR channels (Gordon and Wang, 1994). Specifically,
these approaches compare observed and pre-calculated radiances or polarized
radiances from lookup tables to estimate aerosol optical properties, assuming
that the ocean surface reflectance can be empirically estimated or
neglected. For example, the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 5 operational over-ocean algorithm specifies zero
water-leaving radiance for all channels (550, 650, 860, 1240, 1600, and
2120 nm), except at 550 nm, where a value of reflectance 0.005 is assumed (Remer et
al., 2005). These assumptions are generally reasonable due to the high
absorption effect of seawater in or beyond the NIR bands in which the ocean
surface can be assumed to be black. However, there is still about 50 %
discrepancy in the mean AOT from several prominent aerosol products over
the ocean, with the differences appearing both in terms of magnitude and
temporal tendency (Li et al., 2009). Apart from the different calibration or
cloud screening schemes used in different algorithms, correction of the
surface effect is one of the main factors causing such discrepancy (Li et
al., 2009). As for the aerosol retrieval at shorter bands or in turbid
waters, the backscattering of oceanic particulates could be higher as a result of contributions from the underwater field to the satellite-observed
reflectance should be accounted for. To further consider the effects of
oceanic substances in the retrieval of aerosols, other studies have been
conducted to simultaneously derive AOT and water-leaving radiance using
coupled atmosphere–ocean radiative transfer models (Doerffer and Fischer,
1994; Stamnes et al., 2003; Fan et al., 2017; Shi and Nakajima, 2018), or a
sea surface reflectance model (Sayer et al., 2010), as well as the combined
polarization information (Hasekamp et al., 2011; Knobelspiesse et al., 2012;
Gao et al., 2018).

Like most satellite retrievals, the aerosol inversions are performed over
single pixel, one at a time, before independently moving to another pixel, independently. To
overcome the deficiency of the possibly limited information contained in a
single pixel regarding all the retrieved parameters, Dubovik et al. (2011)
develop a generalized aerosol retrieval system known as the Generalized
Retrieval of Aerosol and Surface Properties (GRASP) to derive aerosol
properties, which uses polarization and multi-angle, multi-wavelength, and
multi-pixel information integrated into a sophisticated statistically
optimized scheme, based on the assumption that the variations of retrieved
parameters are horizontally and temporally smooth from pixel to pixel and/or
from day to day. A similar horizontal constraint scheme based on the adjacent
pixel information has also been adopted in the retrieval of aerosol and
water-leaving radiance over the open ocean (Xu et al., 2016), as well as a
new correlated multi-pixel inversion approach based on the principal
component analysis (Xu et al., 2019). Since these algorithms adopt
polarization and multi-angle measurements that many imagers cannot provide,
Hashimoto and Nakajima (2017) develop a satellite remote-sensing algorithm
to retrieve aerosol properties using multi-wavelength and multi-pixel
information (MWMP). Adhering to the implementation of Hashimoto and Nakajima (2017), who implement aerosol retrieval over land, in this study, we
investigated the potential value of a multi-pixel scheme combined with
multiple wavelength information in the remote sensing of aerosols over
several oceanic conditions, i.e., both open and coastal waters, as well as
over the land–ocean interface region.

In this study, we firstly use a well-established coupled atmosphere–ocean
radiative transfer model to simulate the spectral measurements, namely those of the Greenhouse
Gases Observing Satellite and Thermal and Near Infrared Sensor for Carbon
Observation – Cloud and Aerosol Imager (GOSAT∕TANSO-CAI, hereafter
referred as CAI), in four bands for two cases of open and coastal waters.
Statistical samples of the MODIS ocean color data selected from two
representative regions in the Lanai and Yellow seas are adopted to model the
underwater optical properties in the simulation retrieval experiment. Then,
we use the optimal estimation theory to investigate the effects of the
multi-pixel scheme on the retrieval of aerosols by studying various
numerical results in different ocean conditions. Finally, we conduct the
retrievals based on the real CAI measurements and make comparisons with
those from the MODIS standard aerosol products and in situ observations from the
Aerosol Robotic Network (AERONET; Holben et al., 1998; Dubovik and King,
2000).

In the atmosphere and ocean system, the satellite-received multispectral
radiance or reflectance vector at a subdomain of an imagery with multiple
pixels can be expressed as y, with the dimensions of Nλ×Nu×Nv, where Nλ is the number of measured
wavelengths, and Nu and Nv are the numbers of pixels in two
horizontal orthogonal directions of the subdomain, respectively. The
measurement vector can be related to the state vector x and error
ε as follows:

(1)y=F(x)+ε,

where x denotes the set of unknown parameters in the subdomain with
the dimensions of Np×Nu×Nv. Here, Np is the
number of parameters being retrieved in each single pixel, and F(x)
is the forward radiative transfer model, which describes the knowledge of
the measurement process and physics of the problem. ε
is the error vector that consists of the measurement and model errors. The
inversion problem is deriving x from observation y by
inverting the forward model F at a subdomain, i.e., simultaneous
determination of the retrieved parameters with number of Np in each
pixel of the subdomain with dimensions of Nu×Nv. Since the
inversion is often an ill-posed problem, a prior constraint for the state
vector is usually considered. Moreover, assuming that the aerosol loading is a
slowly variable function of the horizontal direction (Dubovik et al., 2011;
Hashimoto and Nakajima, 2017), as is the chlorophyll a concentration (Chl; Xu et al., 2016), and is extended to the sediment and colored dissolved
organic matter (CDOM), which are more conspicuous in turbid waters, a spatial
smoothness constraint on the variation of aerosol and oceanic substances can
be added during the retrieval. If we treat the forward model as linear in
the vicinity of the true state, the inversion tends to solve the equation
set as follows:

(2)y=Kx+ε,x=xa+εa,0=Bu+Dux+εu,0=Bv+Dvx+εv,

where K is the Jacobian matrix expressing the sensitivity of the
model to an infinitesimal change in each retrieved parameter as
K=∂y/∂x, xa is the a priori
estimate of the state vector before retrieval, and εa
is the a priori error. Bu and Bv are the
boundary conditions in which values are determined from the neighboring
subdomains; Du and Dv comprise the second differential
coefficient matrix given by the Phillips–Twomey method (Phillips, 1962;
Twomey, 1963), and these are adopted as smoothness constraints in each
horizontal direction of the subdomain; εu and
εv indicate the uncertainties of these derivatives
in the u and v directions, respectively. It should be noted that this
type of smoothing constraint has also been used in the retrieval of aerosol
size distribution derived from the ground-based measurements of AERONET and
SKYNET (King et al., 1978; Nakajima et al., 1996; Dubovik and King, 2000).
Provided that the measurement and a priori error are characterized by a
Gaussian probability distribution function, the inversion can be changed to
minimize the cost function as follows:

ϕ=y-KxTSε-1y-Kx+x-xaTSa-1x-xa+γuBu+DuxTBu+Dux+γvBv(3)+DvxTBv+Dvx,

where γu and γv denote Lagrange multipliers, which
represent the strength of the spatial smoothness constraint on the norm of
the second derivatives in two horizontal directions. In principle, these two
parameters are interpreted by the reciprocal of the covariance of the
horizontal distribution variation of the state vector in two directions,
whereby the larger the Lagrange multiplier, the stronger the smoothing
constraint. Sε is the measurement error covariance
matrix, and Sa is the variance–covariance matrix estimated by
a priori state values in which the off-diagonal elements are assumed to be 0.
The optimal solution of Eq. (3) can be solved by the Gauss–Newton iteration
method, calculated as follows:

where xi is the state vector to be retrieved at the ith
iteration of the subdomain, and I is the unit matrix with a size of
Np. After several iterations, the retrieved parameters over multiple
pixels at the subdomain can be converged and derived simultaneously. It
should be noted that when the Lagrange multipliers, i.e., γu and
γv, are zero, which means that no spatial smoothness constraints are
implemented in the retrieval, Eq. (4) is changed to the typical solution of
the maximum a posteriori method used in the traditional single-pixel
retrieval (Rodgers, 2000).

In this study, we use a coupled atmosphere–ocean vector radiative transfer
model, i.e., Pstar, for the forward radiation calculation (Ota et al.,
2010). Pstar was originally developed for the simulation of radiative
transfer in the coupled atmosphere–ocean system by accounting for the
polarization effects. It is developed based on the scalar version of Rstar
(Nakajima and Tanaka, 1986, 1988) and was improved by Shi et al. (2016) to
simulate the radiation process in turbid waters by combining a
three-component bio-optical ocean module and water-leaving radiance
calculation scheme. The accuracy of the radiative transfer scheme in the model
has been proven by a serious intercomparison from IPRT (International
Radiation Polarized Radiative Transfer; Emda et al., 2015) in the
atmosphere and the standard underwater radiative transfer problem in the
ocean system provided by Mobley et al. (1993) (Shi et al. 2015).

For the aerosol modeling, we adopted a sophisticated scattering approach
that combines external and internal mixture schemes. It is assumed that
three kinds of aerosol modes, i.e., fine, sea salt and dust, exist in the
atmosphere, of which each mode grows and changes its refractive index with
increasing humidity independently (external mixing). Moreover, an internal
mixture of water-soluble, dust-like, and soot exists within the fine aerosol
(internal mixing) of which the refractive index is calculated by the sum of
each internal component contribution based on its volume fraction. It should
be noted that the dust aerosols are considered to be non-spherical, and the
scattering phase matrix is calculated using Dubovik et al.'s (2002)
method. Since the CAI has only four spectral bands without multi-angle or
polarization information, the size distribution for each mode is fixed in
this study with log-normal assumption (Shettle and Fenn, 1979), even
though they differ from pixel to pixel in reality and a Gamma distribution
for sea salt aerosol might be more appropriate (Yu et al., 2019). However, a
comprehensive retrieval experiment covering different ocean regions has
demonstrated the reasonability of this assumption in the retrieval of the AOT
and water-leaving radiance based on the systematic comparison with those
from AERONET OC measurements (Shi and Nakajima, 2018).

For the ocean, we assume a four-layer system of infinite depth coupled with
a wind-generated rough surface model in which the reflectance and
transmission matrices are calculated based on the scheme of Nakajima and
Tanaka (1983). Moreover, a three-component bio-optical ocean module is
implemented to model the inherent optical properties (IOPs) of oceanic
substances, i.e., Chl, sediment, and CDOM (Shi et al., 2016). To model the
IOPs of seawater, particularly in the UV bands, we used newly compiled data
from Lee et al. (2015), which have provided better closure for the remote-sensing reflectance (Rrs), i.e., the ratio between the water-leaving radiance
and the downward irradiance just above the ocean surface, in the UV-visible
domains. It should be noted that we use the Rrs instead of the water-leaving
contribution to the satellite-received radiance due to its important effect
on the ocean color retrieval in this study.

4.1 Retrieval using synthetic measurements

We focus on the retrieval from the GOSAT∕TANSO-CAI. GOSAT is mainly designed
to measure the carbon dioxide loading using the TANSO Fourier Transform
Spectrometer. In addition, the satellite carries the Cloud and Aerosol
Imager (CAI) with four channels (380, 674, 870, and 1600 nm), ranging from
UV to SWIR bands for cloud screening and aerosol detection. We firstly
simulate the synthetic measurements from the CAI in four spectral bands
(Nλ=4) based on the improved Pstar model. Moreover, we define a
5×5 pixel region as one subdomain, i.e., Nu/v=5, though there
is no limitation in these definition if the computer resource is allowed.
The geometric information is determined by the mean values of the CAI
observations at the solar zenith angle of 27∘±1, satellite
zenith angle of 30∘±1, and relative azimuth angle of
150∘±1 at the subdomain (Hashimoto and Nakajima, 2017).

The simulated true AOT values at 500 nm for each mode are given as 0.02,
0.1, 0.2, and 0.3, respectively. The total AOT is the sum of each AOT in a
random mixture. We defined the soot fraction in fine aerosol as randomly
ranging from 0.5 % to 1.5 %. In the ocean surface, a moderate wind speed
of 5 m s−1 is assumed. From the widely used suite compiled by the NASA
Ocean Biology Processing Group, and based on the large statistical ocean
color sample of MODIS, we selected two representative classes of oceanic
scenarios: the Linai region, in which the water is typically clear, with
climatological values of Chl, a_443, and bbp_443 being about 0.056 mg m−3, 0.017, and 0.0014 m−1,
respectively, and the Yellow Sea, in which the water is typically coastal,
with climatological values of Chl, a_443, and
bbp_443 being about 3.00 mg m−3, 0.35, and 0.039 m−1, respectively, where a_443 denotes the total
absorption coefficient of ocean at 443 nm, and bbp_443 is the
total backscattering coefficient of oceanic particulates at 443 nm. It
should be noted that the used Chl products are derived by the OCI algorithm
of Hu et al. (2012), and a_443 and bbp_443
products are derived by the quasi-analytical algorithm (QAA) method of Lee et al. (2002), respectively.
We assume the aerosol and oceanic-substance spatial distributions to be
homogeneous in the 5×5 pixel regions. In total, we have 64
atmospheric cases of simulated observation data with a Gaussian random noise
of 2 % standard deviation as measurement errors for each oceanic
condition. Then eight parameters of each pixel, i.e., AOTs of fine, sea
spray, and dust; the volume soot fraction in fine aerosol; wind speed; and
concentrations of Chl, sediment, and CDOM for the whole subdomain, are
determined simultaneously using Eq. (4). The soot fraction in fine aerosol
is defined as the retrieval parameter owing to its high absorption effects.
The a priori conditions are randomly defined in a ±50 % range of the
true values, except for the soot fraction, which has a fixed value of 0.01.
To investigate the feasibility of the multi-pixel method in the retrieval, we
analyzed the simulation data, adopting different γ values of 0.0,
0.1, 0.5, 1.0, 1.5, 2.0, and 3.0. The general simulation and retrieval setup
are summarized in Tables 1–2.

Table 1Aerosol and oceanic mode used in this study.

* The volume size distribution of aerosol particles is assumed to follow
a log-normal function, dVdlnr=V2πexp-(lnr-lnrmv)22σv2, where V is the
aerosol volume density, rmv is the median radius, and σv
is the standard deviation.

Figure 1 shows the retrieved AOT and spectral Rrs values with true
conditions as well as the statistical results of the retrieved relative
error and root-mean-square deviation (RMSD) at different values of γ
for the open ocean. Note that Fig. 1a–g show only the retrievals of 0.0
and 3.0 at γ, which denote the use of no spatial smoothness
constraint, i.e., the traditional single pixel method, and allowed a
variation of about 1.35 times the retrieved parameters constrained from
neighboring pixels, respectively. The results indicate that the accuracy of
the retrieved AOT of each mode is generally improved by using the spatial
smoothness constraint, i.e., the multi-pixel method, to correct the
retrieval bias induced by measurement errors. Specifically, the retrieved
relative error and RMSD of the fine AOT decrease from 30.51 % and 0.031 to
13.45 % and 0.018, respectively, when the γ values change from 0.0
to 3.0 (Fig. 1h–i), which indicates the effectiveness of the multi-pixel
method in aerosol retrieval. Coarse aerosols (sum of sea spray and dust) can
also be well derived, which is partly due to the adoption of the SWIR
channel observation (Fig. 1e), even though larger errors are shown for the
inversion of each coarse aerosol, i.e., AOT of sea spray and dust (Fig. 1b–c), compared with the true values. Additionally, due to the more
significant improvement in the retrieval of the fine AOT, the multi-pixel scheme
contributes to a better estimation of the total AOT (Fig. 1f). In contrast,
the soot fraction is difficult to retrieve due to its low sensitivity to
measurements, even though an UV channel observation, i.e., 380 nm, is
implemented by the CAI, for which the retrieval results are highly dependent
on the a priori value (1 % in this case; Fig. 1d). In regard to the
spectral Rrs, we find that the multi-pixel method helps to facilitate the
consistency of the retrieval with the true values (Fig. 1g) in comparison to
those derived by the single pixel method, and this finding is similar to
that of Xu et al. (2016) over open oceans. The low values of Rrs at 860 nm
and at 674 nm also support the reasonability of our previous black ocean
assumption in those bands in the two-channel aerosol inversion (Nakajima and
Higurashi, 1997). However, the underwater influence in the retrieval of
aerosols at UV channels over the open ocean is suggested to be considered
due to the higher backscattering effect of ocean body.

Over coastal waters, the sediment and CDOM, which exist with higher
concentrations in the ocean and show generally similar inherent optical
properties to the fine aerosol and soot, exert non-negligible effects on the
aerosol retrieval. Compared with the inversion of fine AOT over the open
ocean (Fig. 1a), the retrieval in the low-aerosol loading over coastal
regions shows larger biases when using the traditional single-pixel method,
mainly due to the contamination of oceanic sediment (Fig. 2a). Nevertheless,
retrieval errors can be effectively reduced using the multi-pixel scheme,
with the relative error and RMSD decreasing about 27.4 % and 0.02234
(Fig. 2k–l), respectively. This
improvement is also due in part to the better estimation of the spectral Rrs
(Fig. 2j). It is demonstrated that the retrieved accuracy of the coarse AOT is
generally similar to that in clear waters (Fig. 2e), which is partly
attributable to the utilization of SWIR measurements that are not sensitive
to sediment and can be used in the atmospheric correction over turbid waters
(Wang and Shi, 2007). Moreover, it remains difficult to retrieve the
absorptive soot over coastal waters, even when using the multi-pixel
constraint (Fig. 2d). With regard to the underwater retrieval, significant
improvements are evident in the inversion of oceanic substances,
particularly for the sediment and CDOM, after implementing the spatial
smoothness constraint (Fig. 2g–i). Such improvements also contribute to
the better retrieval of the spectral Rrs, with the relative errors in the
first three CAI bands decreasing from 41.87 %, 17.76 %, and 15.94 % to
22.87 %, 8.09 %, and 8.23 %, respectively. Generally, there are higher
averaged kernel matrix values for fine and coarse aerosols, sediment, and
CDOM than those for the soot fraction, Chl, and the wind speed in
the non-glint cases during the retrieval. It should be noted that we used
relatively accurate a priori values for the AOT estimation in a range of
±50 % of the true conditions, however, the retrieved sea spray and
dust will have larger biases when xa exceeds true values more
largely, owing to the limited spectral information of CAI and similar
optical properties of these two modes. However, their sum, i.e., the total
coarse AOT, can still be determined well and exhibits no obvious dependence
on the a priori conditions.

Figure 3Simulation experiment for AOT retrieval of fine
and coarse aerosols, spectral Rrs with (blue points denoted as MP
with γ values of 1.0) and without (orange points
denoted as SP) multi-pixel constraints over inhomogeneous areas
from coastal to open-ocean regions (a–c), and retrievals from land (ground
covered by reddish-brown fine sandy loam) to coastal ocean regions (d–f).
The purple line of (f) is the boundary line with AOT_Fine at
500 nm of 0.1 (right part of boundary line denotes retrieval under the
condition of AOT_Fine greater than 0.1, and vice versa). The
red line of (f) shows the a priori values used in this simulation. The
retrieved soot fractions over the ocean nearest to the coastal line are denoted by
solid circle in (f). Land surface reflectances at 380, 674, 870, and 1600 nm
are 0.1098, 0.2775, 0.3630, and 0.4790, respectively.

Figure 4Retrieved volume soot fraction in the fine
aerosol over the coastal ocean with the condition of homogeneous aerosol
distribution for the land–ocean interface region; (a) is the retrieval with
AOT of fine > 0.1, and (b) is the retrieval with AOT of fine
> 0.1 and ratio of fine AOT > 0.5. The red line shows
the a priori values used in this simulation.

The above results demonstrate the effectiveness of the multi-pixel scheme in
the retrieval of aerosols over homogeneous atmosphere–ocean areas. To
consider the retrieval under inhomogeneous conditions, we conducted further
inversion experiments in two situations. First, we assumed that the aerosol
loading and oceanic substances change continuously from coastal to open
ocean, with a large spatial variation in the 5×5 pixel subdomain.
Results indicate that the multi-pixel strategy still performs better
retrieval in this case, as shown in Fig. 3a–c, particularly for the
estimation of fine aerosols. Similar to the retrievals over the homogeneous
region, the spectral Rrs can be better derived using the multi-pixel scheme,
especially over coastal regions (low values of the Rrs at 380 nm and high values
of the Rrs at 674 nm), but the traditional single-pixel method tends to yield
larger bias estimations for the retrieval (Fig. 3c). Another inversion
experiment is performed for the retrieval over land (with a higher aerosol
loading and soot fraction) and coastal ocean interface regions in the
subdomain. In this simulation, the land surface is assumed to be reddish-brown
fine sandy loam with spectral reflectance values of 0.1098, 0.2775, 0.3630,
and 0.4790 for the four CAI bands, and values are selected from
the ECOSTRESS spectral library (https://speclib.jpl.nasa.gov/library, last access: 15 February 2019). For the aerosol retrieval over
land, we make simultaneous determinations of the AOT and spectral surface
reflectance (Ag) with randomly defined a priori values of Ag in a
range of ±10 % of the true conditions and assumed spectral
uncertainties of 0.02, 0.02, 0.02, and 0.001 for the CAI channels,
respectively. The results indicate that the single-pixel method generally
overestimates the fine and coarse AOT values over sand due to the high
ground reflectance. However, the retrieval accuracy over the sand surface
improves significantly by constraining the spatial aerosol variation in the
subdomain, which also benefits from the better AOT estimation over the
coastal ocean region (Fig. 3d–e). With regard to the retrieval of the soot
fraction (SF; Fig. 3f), it remains difficult to derive over-ocean areas
with a high dependence on the a priori value (red line of Fig. 3f), whereas
absorptive soot can be better estimated over land regions due to the high
reflectance of the ground surface by providing more significant information
to the retrieval. Moreover, the multi-pixel scheme promotes the inversion of
the SF, particularly in high aerosol conditions, which is similar to the
research of Hashimoto and Nakajima (2017) conducted over the whole land
regions. The performance of retrieval for absorptive soot with dependence on
the aerosol loading over the land, where the better retrievals are
identified in the condition of fine AOT at 500 nm over 0.1 (Fig. 3f) in this
study, also supports the finding that errors of retrieved single scattering
albedo decrease with increasing AOT for the AERONET (Dubovik et al., 2000).
It is interesting that the retrieved accuracy of the SF nearest to the coastal line
over the ocean (solid circles of Fig. 3f) tends to be improved using the
multi-pixel method, though it is slightly improved. This improvement is more
significant in the homogeneous aerosol distribution and dominated fine-mode
conditions over the land–ocean interface region, as shown in Fig. 4. The
availability of retrieval for the absorptive soot over the dark surface, i.e.,
the ocean region, benefits from the spatial smoothness constraint from the
better-derived SF over the bright surface, i.e., sand ground, where the
surface albedo is near or over the neutral reflectance defined by Kaufman (1987). We then derived the relationship between the neutral reflectance
(An) in which the apparent reflectance does not change with AOT and
the single scattering albedo (ω), asymmetry factor (g), and phase
function (P(cos Θ)) of aerosols based on the single scattering and
two-stream approximation over land, calculated as follows:

(6)An=πωP(cosΘ)μμ0t^(μ)+t^(μ0);t^(μ)≡m1-ω121+32gμ,

where μ and μ0 are the cosines of the satellite and solar
zenith angle, respecitvely. It is demonstrated that the neutral reflectance of band 2 of
the CAI is ranged from 0.232 to 0.275 when the asymmetry factor and phase
function are 0.7 and 0.0142, respectively, corresponding to the single
scattering albedo of 0.935 and 0.950 with the soot fraction of 2.05 % and
5.10 %, which is generally similar to the threshold values of the retrieved
SF in Figs. 3f and 4b. However, these threshold values are just the
specific case used in this study and are also dependent on the ratio of fine AOT
in real conditions.

4.2 Retrieval using real CAI measurements

Following the simulation retrieval experiment performed using synthetic
spectral measurements, we then apply the proposed algorithm to the real CAI
data for deriving aerosols over the ocean. Radiometric correction was conducted
as prescribed in Shiomi et al. (2010). With regard to the ancillary data,
we use the surface pressure and wind speed data from the National Centers
for Environmental Prediction (NCEP) to correct the Rayleigh scattering and
sea surface reflectance, respectively, as well as the relative humidity data
to account for the effect of aerosol hygroscopic growth. The gas absorption
is processed by a correlated k-distribution approach (Sekiguchi and
Nakajima, 2008) where several main absorptive gases are considered, and
the column ozone data are adopted from the ozone monitoring instrument (OMI).
In particular, we used a relatively high spatial smoothness constraint with a
γ value of 1.0 for each horizontal orthogonal direction in the
multi-pixel scheme. Moreover, to keep the consistency between each
subdomain, the boundary conditions of Bu∕v used in Eq. (4) are
determined by the retrieved results derived from the neighbor subdomains.

Figure 5Spatial distributions of retrieved fine, coarse,
and total AOTs from CAI measurement on 13 March
2012 using traditional single-pixel method (denoted as SP) and
multi-pixel scheme (denoted as MP).

Figure 5 compares the spatial distributions of retrieved fine, coarse (sum
of sea spray and dust), and total AOTs using single- and multi-pixel
methods. Results show that the derived AOTs by the single-pixel approach
have a generally similar spatial distribution to those retrieved by the
multi-pixel method, which the fine aerosol dominates. However, irregular
dotted variations with abnormal retrieval results are shown in some pixels
(black box in Fig. 5) when conducting the single-pixel retrieval. Although
it is difficult to support these irregular dotted distributions being real,
the investigation of the posterior error in those pixels demonstrates that
the retrieved uncertainties are generally higher than those of other pixels
(not shown). Such kinds of occasionally irregular dotted variations derived by
the single-pixel method have also been identified in the aerosol retrieval
over land (Hashimoto and Nakajima, 2017), which we rather consider to be
caused by errors in the single-pixel inversion that tends to be affected by
various observation noises. On the contrary, the multi-pixel scheme is more
robust to these factors, so the irregular dotted variation of retrieved AOT
can be effectively improved when considering the spatial smoothness
constraint during the retrieval, as shown in Fig. 5d–f, which allows
reduction of the retrieval errors constrained by adjacent pixels.

Figure 6Monitoring of the Asian dust event from CAI and MODIS.
Spatial distribution of CAI-derived AOT for fine and coarse aerosols from
the single-pixel method (a–b), multi-pixel method (d–e), and the
MODIS Terra aerosol Level 2 products (c and f) on
27 April 2012 over the Yellow Sea.

Another retrieval experiment is performed on the monitoring of the Asian
dust event from the CAI. Studies have demonstrated that dust aerosols
carried by the dust storm in East Asia exert significant influence on the
local ecosystem and environmental pollution (Huang et al., 2014). Figure 6
shows the spatial distribution of retrieved fine and coarse AOTs from the CAI on
27 April 2012 over the Yellow Sea. In order to have a better
validation for the current algorithm, the MODIS standard Level 2 aerosol
products derived using more channels, with the satellite overpass time about
3 h later than that of the CAI, are also adopted as comparison. Results
show that a relatively obvious transport belt for fine aerosols between the
south of the Shandong Peninsula and the middle of the Yellow Sea is derived by the
CAI (Fig. 6a); meanwhile, significant dust storms are determined in the
north of Yellow Sea (Fig. 6d), where the retrieved coarse AOTs at 500 nm
are over 1.5 in the high-density areas. It is demonstrated that the derived
AOTs for fine and coarse aerosols are generally consistent with the MODIS
standard aerosol products with similar spatial distributions (Fig. 6c and f).
In addition, the derived AOTs from the CAI with the multi-pixel method (Fig. 6b and e) around the Shandong Peninsula are in more agreement with MODIS
aerosol products than those retrieved by the single-pixel approach, which
implies the effectiveness of the multi-pixel scheme in the inversion of
aerosols, particularly for fine aerosol. It should be noted that the derived
fine AOT values from the CAI seem to be generally lower than those obtained
using MODIS products over the Yellow Sea. Although our algorithm divides the
coarse aerosols into sea spray and yellow sand, it is more appropriate to use
their sum, i.e., coarse AOTs, than the yellow sand as the indicator of the
Asian dust transport, since the retrieval errors of coarse AOTs determined by
the CAI are much lower than those of individual yellow sand particles, as shown in Fig. 2c and e. Such a deficiency in distinguishing the sea spray and dust is
expected to be better improved using the upcoming Cloud and Aerosol Imager 2
(CAI2) with seven channels (340, 380, 443, 550, 674, 869, and 1630 nm) by
providing more measurement information.

Figure 7Comparison of CAI-retrieved total AOT by the
single-pixel method without or with the SWIR band, i.e., 1600 nm (a and d,
respectively), with those from the multi-pixel method without or with the SWIR
band (b and e, respectively), and the spatial distributions of
MODIS Aqua Level 2 AOT products (c) and satellite-received reflectance at
band 4 of CAI (f) on 3 December 2013.

Retrieval of aerosols over extremely highly turbid waters is still a challenging
problem due to the significant contamination from the backscattering of
oceanic particulates, currently. Taking the Hangzhou Bay (HZB) as a sample
region, the total suspended particulate matter can be over 1000 mg L−1
sometimes (He et al., 2013), which contributes a substantial proportion into
the satellite signals as a result of the aerosol being generally difficult
to accurately derive. In order to investigate the feasibility of
the multi-pixel scheme in the retrieval of the AOT over highly turbid water, we try to
apply the current algorithm in such a circumstance. Figure 7 shows the comparison
of the retrieved total AOT by using the single- and multi-pixel method with or without
using the SWIR band of the CAI, i.e., 1600 nm, with those from the MODIS aerosol
products in December–March 2013 over the East China Sea. It should be
noted that there are several high-error observation belts for band 4 in this
image (Fig. 7f) due to some instrument problems, but the data are available
for most regions including the HZB. Results demonstrated that the retrieved AOTs
by the CAI with or without using the SWIR measurement are all consistent with
those of the MODIS aerosol product (Fig. 7c) beyond the coastlines, however,
the estimated AOTs from the CAI using different strategies around highly turbid
regions show large differences. Generally, the derived AOTs without using
SWIR measurements (Fig. 7a) demonstrate obviously higher values than those
retrieved by adding SWIR information (Fig. 7d) near coastal region. This is because the satellite reflectance at SWIR channels is much less
sensitive to the suspended sediment than that at visible bands in turbid
waters, so the aerosols can be estimated without significant
contamination of sediment (Wang and Shi, 2007) based on the SWIR
observation. Although we simultaneously conduct the oceanic sediment
retrieval in the algorithm, it is still difficult to use four spectral
measurements to estimate at least five free variables (AOT of fine, sea spray
and dust, sediment, and CDOM) in the high backscattering surface condition,
where the retrieval could be degenerated. Nevertheless, such a deficiency can
be improved using the multi-pixel scheme even though the SWIR measurements
are not used (Fig. 7b), which indicates the potentiality of the multi-pixel
strategy in the aerosol retrieval over highly turbid waters, particularly for
those multispectral instruments without the SWIR observation.

Figure 8Comparison of retrieved AOT values for fine,
coarse, and total aerosols at 500 nm from CAI with those from AERONET
observations. Circles and crosses indicate the retrieved values at pixels
closest to AERONET sites with or without multi-pixel method implementation,
respectively. Orange dotted lines denote a priori values.

To further investigate the feasibility of this algorithm, two in situ data from the AERONET, i.e., the Ieodo Station and
Gageocho Station, are used for the validation. To examine the
dependence of this retrieval on the a priori information, we set fixed values
of xa for all cases. We selected the retrieved AOTs from
the pixel closest to the AERONET site in the subdomain. The results indicate
that the retrieved AOT values for fine and coarse aerosols, as well as the
total aerosols, are all consistent with those of the AERONET observations
without significant dependence on the a priori information (Fig. 8). It should
be noted that the simultaneous retrieved AOTs for fine and coarse aerosols
are denoted in same color. Generally, increased accuracy in the determination
of AOTs is demonstrated by using the multi-pixel method (shown by circles),
with the retrieved relative errors of the AOT for fine, coarse, and total aerosols
decreasing from 26.19 %, 96.70 %, and 27.64 % to 23.52 %, 86.83 %, and
22.40 %, as well as the RMSD, which varied from 0.1062, 0.05660, and 0.1129 to
0.06838, 0.04960, and 0.08738, respectively, in comparison to those derived by
the single-pixel scheme (shown by crosses). As in the simulation inversion
experimental results shown in Figs. 1–3, the multi-pixel scheme tends to
be more effective in the retrieval of fine aerosols than of coarse aerosols from the
CAI measurements. However, we still identify a few cases in which the retrieved
errors have increased using the multi-pixel scheme, which inspires us to make
further studies on the better definition of γ values for each
retrieved parameter or the pixel resolution of the subdomain. It should be noted
that we neglect the multiple scattering influence between neighbor pixels
caused by the adjacent effect in the retrieval, since the effect is generally
small for the CAI instrument with moderate spatial resolution. Nevertheless,
we have to consider the adjacent effect for the extremely high spatial
resolution imagers using a 3-D radiative transfer model.

In this work, we focused on the aerosol retrieval from multi-pixel and
multispectral satellite observations from the CAI over the ocean. Unlike most
algorithms that conduct the aerosol retrieval pixel by pixel, we derive
aerosol properties of multiple pixels simultaneously by considering the
smoothness constraint on the spatial variation of aerosols and oceanic
substances between the pixels, i.e., the multi-pixel method. We firstly
investigated the availability of the multi-pixel scheme in the conditions of
open and coarse ocean as well as the land–ocean interface region based on
the synthetic measurements of the CAI. Results indicate that the multi-pixel
scheme improves the aerosol inversion by increasing the retrieval
sensitivity and correcting the retrieval bias induced by measurement errors
over multiple pixels, particularly for the fine aerosol over coastal
regions. In addition, the spectral remote-sensing reflectance can be also
derived with a higher accuracy by constraining the spatial variation of
components in the ocean. We then apply the current algorithm using real CAI
measurements. The image analysis demonstrates that the irregular retrieved
results can be effectively improved using the spatial smoothness constraint.
In addition, the multi-pixel scheme shows promising potentiality to retrieve
the aerosols over highly turbid waters, especially for those instruments
without SWIR measurements. In comparisons with the AERONET observation,
retrievals using the multi-pixel scheme tend to be more consistent with the
measurements than those derived by the single-pixel method.

Although we compared retrievals using different Lagrange multipliers values
in this study, these parameters have similar roles of covariance of
the state vector and should be decided by observed variables or
information from high-resolution instruments for the spatial smoothness
constraint, which needs more analysis. It is demonstrated that the
multi-pixel scheme shows a promising technique in the aerosol and hydrosol
retrieval based on the multiple source constraints from satellite
observation, a priori, and neighbor pixel information in an iteration manner.
To apply the scheme used in the global ocean, we have constructed a neural
network solver to accelerate the algorithm, and a related study will be
explicated in another work. Moreover, investigation regarding the
multi-pixel scheme's retrieval performance over the sun-glint area is also a
part of our future work. Actually, the retrieved results shown in Fig. 6 are
contaminated by the sun glint to some extent, with the glint angles mostly
ranging from 25 to 40∘ of the imagery. As in our previous
study in which the simultaneous adjustment of the wind speed value helps the aerosol
retrieval over the sun-glint region by correcting the surface reflectance
(Shi and Nakajima, 2018), the retrieved AOTs of fine and coarse aerosols from
the CAI show general consistency with those of MODIS products without sun-glint
contamination (Fig. 6). Nevertheless, it seems that the retrieved fine AOTs
are still lower than those of the MODIS products overall, which also
inspires us to make a further study on the application of multi-pixel scheme
in this issue.

CS wrote the paper and algorithm codes and analyzed the data. TN designed all the research.
MH helped with the algorithm development and CAI data usage. The scientific contributions were provided by all coauthors.

This work was
supported by funds from MOEJ–JAXA/GOSAT–GOSAT2, JST/CREST/ JPMJCR15K4,
JAXA/EarthCARE–GCOM-C, and MOEJ/ERTDF/S-12. One of author
was supported by the National Natural Science Foundation of China (NSFC;
41590875, 41571130024) and the Key Laboratory of Meteorological Disaster of
the Ministry of Education at the Nanjing University of Information Science
and Technology (KLME1509). The authors express their sincere thanks to the relevant
PIs (Young-Je Park, Hak-Yeol You, Jae-Seol Shim, Joo-Hyung Ryu) for establishing and
maintaining the AERONET sites used in this investigation. We also appreciate
the GOSAT, NCEP, OMI, MODIS, ECOSTRESS science teams for releasing data used
in this analysis. GOSAT/TANSO-CAI data are provided by JAXA/NIES/MOE. NCEP
Reanalysis data are provided by the NOAA. OMI data are provided by NASA.
MODIS ocean color products are provided by the NASA Ocean Biology Processing
Group. Land surface spectral reflectance data are provided from the ECOSTRESS
spectral library of JPL/NASA. We also thank Kei Shiomi for providing
GOSAT/TANSO-CAI calibration material, as well as insightful suggestions, to
improve our work.

Shettle, E. P. and Fenn, R. W.: Models for the Aerosols of the Lower
Atmosphere and the Effects of Humidity Variations on Their Optical
Properties, Air Force Geophysics Laboratory, Hanscom Air Force Base, MA, USA,
1979.

This paper presents a new technique for retrieving aerosol optical properties using multi-wavelength and multi-pixel information over the ocean. Different from the traditional satellite aerosol retrievals conducted pixel by pixel, we derive the aerosol optical properties of multiple pixels simultaneously by adding a smoothness constraint on the spatial variation of aerosols and oceanic substances. The technique asserts that the multi-pixel scheme is conducive to aerosol retrieval over the ocean.

This paper presents a new technique for retrieving aerosol optical properties using...